与式（2.114）类似的球形卷积方程的完整讨论，包括傅里叶变换关系的发展，在Baddour（2010）一文中给出。

A full discussion ofa spherical convolution-like equation similar to Eq. (2.114), includingdevelopment of the Fourier transform relations, is given in Baddour (2010).

然而，与线性卷积一样，式（2.117）将空间中给定点的输出计算为反射率分布的局部平均值，由天线方向图和波形进行加权。

Nonetheless, like alinear convolution, Eq. (2.117) computes the output at a given point in spaceas a local average of the reflectivity distribution, weighted by the antennapattern and waveform.

对于大多数天线和脉冲信号，这些方向图将它们的大部分能量集中在一个相对较小的有限区域，该区域由天线方向图的主瓣和波形的脉冲持续时间定义。

For most antennas andpulses, these patterns concentrate most of their energy in a relatively smallfinite region defined by the mainlobe for the antenna pattern and the pulseduration for the waveform.

因此，可以期望输出信号的行为如同真实的线性卷积操作。

Consequently, theoutput signal can be expected to behave like a true linear convolution.

式（2.117）的卷积模型是一个重要结果。

The convolutionalmodel of Eq. (2.117) is an important result.

例如，测量反射率函数的距离分辨率被视为受到脉冲持续时间的限制。

For example, therange resolution of the measured reflectivity function is seen to be limited bythe pulse duration.

（在第4章中，我们将看到引入匹配过滤将显著改变这一描述。）

(In Chap. 4 it willbe seen that the introduction of matched filtering will significantly changethis statement.)

同样，对于传统的扫描雷达，角度分辨率将由天线波束宽度决定。

Similarly, for aconventional scanning radar, the angular resolution will be determined by theantenna beamwidth.

（在第8章中，我们将看到合成孔径技术的引入也显著改变了这种说法。）

(In Chap. 8 it willbe seen that the introduction of synthetic aperture techniques alsosignificantly changes this statement.)

——本文译自Mark A. Richards所著的《Fundamentals of Radar Signal Processing（Second edition）》

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